Two-dimensional optimization of free electron laser designs

Abstract

Off-axis, two-dimensional designs for free electron lasers that maintain correspondence of a light beam with a "synchronous electron" at an optimal transverse radius r>0 to achieve increased beam trapping efficiency and enhanced laser beam wavefront control so as to decrease optical beam diffraction and other deleterious effects.

We claim: 
     
       1. A method for amplification of the optical radiation of predetermined wavelength λ s  =2π/k s  =2πc/ω s  and local electric field strength E s  =√2 mc 2  e s  /e, where e is the unit of electron charge and γmc 2  is relativistic energy of an electron propagating along a predetermined z-axis, the method comprising the steps of: providing a transverse wiggler magnetic field of alternating polarity along the predetermined z-axis, the magnetic field having local field strength B w  =√2 mc b w  /e and local period λ w  =2π/k w  ;   directing a collimated beam of electrons having relativistic energy γmc 2  initially exceeding 2 MeV along the predetermined axis, in timed relationship with propagation of the optical radiation;   providing a substantially constant stable phase angle ψ=∫(k s  +k w ) dz-ω s  t+φ s  associated with the electron beam so that ψ substantially satisfies the relation ##EQU17##  at a radius substantially ##EQU18##  measured transversely from the predetermined electron beam axis, where (2Δγ) m e  c 2  is the representative initial energy spread in the electron beam.   
     
     
       2. A method according to claim 1, wherein the wavelength λ s  is substantially 250 nm, the initial relativistic energy factor γ is substantially 2150, the magnetic field strength is substantially 3.8 kG, the magnetic field period λ w  is substantially 15 cm, the stable phase angle ψ is substantially 0.4 radians, and the laser beam has an initial radius of substantially 0.25 cm. 
     
     
       3. A method for amplification of the optical radiation of predetermined wavelength λ s  =2π/k s  =2πc/ω s  and local electric field strength E s  =√2 mc 2  e s  /e, where e is the unit of electron charge and γmc 2  is relativistic energy of an electron propagating along a predetermined z-axis, the method comprising the steps of: providing a transverse wiggler magnetic field of alternating polarity along the predetermined z-axis, the magnetic field having local field strength B w  =√2 mc b w  /e and local period λ w  =2π/k w  ;   directing a collimated beam of electrons of radius r b  having relativistic energy γmc 2  initially exceeding 2 MeV along the predetermined axis, in timed relationship with propagation of the optical radiation;   providing a substantially constant stable phase angle ψ=∫(k s  +k w ) dz-ω s  t+φ s  associated with the electron beam so that ψ substantially satisfies the relation ##EQU19##  at a radius substantially   r=r.sub.b /√2,        measured transversely from the predetermined electron beam axis.   
     
     
       4. A method according to claim 3, wherein the wavelength λ s  is substantially 250 nm, the initial relativistic energy factor γ is substantially 2150, the magnetic field strength is substantially 3.8 kG, the magnetic field period λ w  is substantially 15 cm, the stable phase angle ψ is substantially 0.4 radians, and the laser beam has an initial radius of substantially 0.25 cm. 
     
     
       5. A method for amplification of the optical radiation of predetermined wavelength λ s  =2π/k s  =2πc/ω s  and local electric field strength E s  =√2 mc 2  e s  /e, where e is the unit of electron charge and γmc 2  is relativistic energy of an electron propagating along a predetermined z-axis, the method comprising the steps of: providing a transverse wiggler magnetic field of alternating polarity along the predetermined z-axis, the magnetic field having local field strength B w  =√2 mc b w  /e and local period λ w  =2π/k w  ;   directing a collimated beam of electrons having relativistic energy γmc 2  initially exceeding 2 MeV along the predetermined axis, in timed relationship with propagation of the optical radiation;   providing a substantially constant stable phase angle ψ=∫(k s  +k w ) dz-ω s  t+φ s  associated with the electron beam so that ψ substantially satisfies the relation ##EQU20##  at a particular radius r=r d  >0, measured transversely from the predetermined electron beam axis, with r d  being determined by substantially maximizing the electron trapping efficiency η t  defined by ##EQU21##  where P o  is laser output power, (Δγ)mc 2  is representative γ initial  -γ final , and i e  is initial electron beam current.   
     
     
       6. A method according to claim 5, wherein the wavelength λ s  is substantially 250 nm, the initial relativistic energy factor γ is substantially 2150, the magnetic field strength is substantially 3.8 kG, the magnetic field period λ w  is substantially 15 cm, the stable phase angle ψ is substantially 0.4 radians, and the laser beam has an initial radius of substantially 0.25 cm.